Question: What do the following two equations represent? $3x+2y = 1$ $15x+10y = -2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x+2y = 1$ $2y = -3x+1$ $y = -\dfrac{3}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $15x+10y = -2$ $10y = -15x-2$ $y = -\dfrac{3}{2}x - \dfrac{1}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.